Semianalytical approach to Ly α multiple-scattering in 21-cm signal simulations

A crucial physical quantity in determining the 21-cm signal during cosmic dawn is the inhomogeneous background of Ly α photons originating from the first galaxies. As these photons travel through the intergalactic medium (IGM), their scattering cross section is often approximated as a delta function at resonance due to computational cost. That is, photons with emitted wavelengths between Ly α and Ly β are assumed to travel in straight lines until they redshift into the Ly α resonance. However, due to the damping wing in the Ly α cross section, this approximation fails as the frequency of the photon approaches the resonant frequency, resulting in multiple scatterings events that could be separated by non-negligible distances. These multiple scattering events effectively modify the intrinsic Ly α emissivity from galaxies. Some previous works studied this effect of Ly α multiple scattering by running computationally heavy radiative-transfer simulations. However, robustly interpreting the cosmic 21 cm signal requires exploring a large parameter space of astrophysical uncertainties, motivating more computationally efficient approaches. Here we incorporate Ly α multiple scatterings in the public, seminumerical simulation 21cm. To do so, we employ Monte Carlo simulations to study the trajectories of Ly α photons on different scales. We find that the distance distributions of Ly α photons with respect to the absorption point can be modeled as analytical functions that are governed by a single parameter. Upon implementing the distance distributions in 21cm, we find that the multiple scattering effect is important (about 50% difference in the 21-cm power spectrum) only at high redshifts before the spin temperature is fully coupled to the kinetic temperature. Furthermore, we find that Ly α multiple scattering does not enhance Ly α heating, and that the combined effect is negligible, especially under realistic x-ray heating scenarios.